Simplify the following expression: $r = \dfrac{t^2 + 7t + 6}{t + 1} $
First factor the polynomial in the numerator. $ t^2 + 7t + 6 = (t + 1)(t + 6) $ So we can rewrite the expression as: $r = \dfrac{(t + 1)(t + 6)}{t + 1} $ We can divide the numerator and denominator by $(t + 1)$ on condition that $t \neq -1$ Therefore $r = t + 6; t \neq -1$